If the west wants to do anything worthwhile toward saving the world system it should adopt an old policy from the middle ages - crusades.
The crusades were necessary to set the stage for the development of western civilization. Had the crusades not stopped the advance of militant Islam there would be no western civilization.
It is apparent to anyone looking at the facts regarding Islam that it is a purely evil force in the world. It does nothing positive. It is repressive. It is cruel. It is maniacle. However, its main evil is that it rejects the concept of human choice. Either a person converts to Islam or they are destroyed.
The aim of Islam is total control as characterized by the term, sharia law. In Islam freedom is anathema. From a human rights perspective the west has every right to destroy such a perverted politico-religious system - not only to protect the non-muslim from its theat but to liberate those muslims who are held captive by it.
Islamic terrorist groups 
- Boko Haram
- Al Queda
- Hamas
- Taliban
- Hezbollah
Only a madman wants war. However, there are some circumstances under which it is necessary and justifiable: for instance, one billion people enslaved to Islam. How about constant fear of atrocities aimed at civilians?
Sadly it is unlikely anything substantial will be done by the west to thwart an inevitable takeover by evil. We don't have the wisdom nor strength in our leadership to do what us in the best interest of humanity. Our leadership had rather joust with windmills (see global warming).
In the event that a leader does arise here's how the war should go forward:
- Propaganda - inundate the populace of the targeted regime with information about what is about to happen.
- Cut Off - The targeted regime would be completely cut off frome the rest of the world. This includes trade, travel and communications. It also includes sending every citizen of the targetted regime back to their country.
- Air lift - Provide food and arms to the populace.
- Reconnaisance - Monitor the progress of the revolution which will naturally occur. When evidence is preponderant that Islam is erradicated the war is over. Note, this may take a generation or more.
Such a war would minimize the west's investment. The cost would be almost completely absorbed by the people who allowed Islam to fester in their country in the first place.